On the relationship between continuous- and discrete-time quantum walk

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this article, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-time quantum walk can be obtained as an appropriate limit of discrete-time quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian oracles; v3: published version, with improved analysis of phase estimatio

New Fundamental dHvA Frequency in Canonical Low-Dimensional Fermi Liquids

We show that a new fundamental period $P_{f}$ of dHvA oscillations, which appears along with other ``forbidden'' combination frequencies in a multi-band canonical Fermi-liquid, is very robust with respect to a finite smearing of Landau levels and a background of non-quantized states. We analyse the possibility of measuring small Fermi surface pockets with the use of the ``forbidden'' frequencies.Comment: 10 pages, RevTeX 3.0, with 2 PS Figure

Quantum random walks with decoherent coins

The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence in the quantum ``coin'' which drives the walk. We find exact analytical expressions for the time dependence of the first two moments of position, and show that in the long-time limit the variance grows linearly with time, unlike the unitary walk. We compare this to the results of direct numerical simulation, and see how the form of the position distribution changes from the unitary to the usual classical result as we increase the strength of the decoherence.Comment: Minor revisions, especially in introduction. Published versio

Blending as a process of creating neologisms in modern English: a study based on electronic media

http://tartu.ester.ee/record=b2694560~S1*es

Carbenicillin-induced coagulopathy

In high dosage, carbenicillin may interfere with the conversion of fibrinogen to fibrin and result in a haemorrhagic diathesis. The effect is dose-dependent and requires a high concentration of carbenicillin in plasma. Such a level may be attained in renal failure unless the dose of the drug is appropriately reduced. In such situations the screening coagulation tests may be prolonged and this should alert one to the development of a haemorrhagic diathesis due to the drug.S. Afr. Med. J., 48, 457 (1974)

Outskirts of Distant Galaxies In Absorption

QSO absorption spectroscopy provides a sensitive probe of both the neutral medium and diffuse ionized gas in the distant Universe. It extends 21cm maps of gaseous structures around low-redshift galaxies both to lower gas column densities and to higher redshifts. Combining galaxy surveys with absorption-line observations of gas around galaxies enables comprehensive studies of baryon cycles in galaxy outskirts over cosmic time. This Chapter presents a review of the empirical understanding of the cosmic neutral gas reservoir from studies of damped Lya absorbers (DLAs). It describes the constraints on the star formation relation and chemical enrichment history in the outskirts of distant galaxies from DLA studies. A brief discussion of available constraints on the ionized circumgalactic gas from studies of lower column density Lya absorbers and associated ionic absorption transitions is presented at the end.Comment: 45 pages, 7 figures, invited review, Book chapter in "Outskirts of Galaxies", Eds. J. H. Knapen, J. C. Lee and A. Gil de Paz, Astrophysics and Space Science Library, Springer, in pres

Quantum Walks driven by many coins

Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum random walk on the line: the use of multiple quantum ``coins'' in order to diminish the effects of interference between paths. We find solutions to this system in terms of the single coin random walk, and compare the asymptotic limit of these solutions to numerical simulations. We find exact analytical expressions for the time-dependence of the first two moments, and show that in the long time limit the ``quantum mechanical'' behavior of the one-coin walk persists. We further show that this is generic for a very broad class of possible walks, and that this behavior disappears only in the limit of a new coin for every step of the walk.Comment: 36 pages RevTeX 4.0 + 5 figures (encapsulated Postscript). Submitted to Physical Review

Planar cell polarity signalling coordinates heart tube remodelling through tissue-scale polarisation of actomyosin activity

Development of a multiple-chambered heart from the linear heart tube is inherently linked to cardiac looping. Although many molecular factors regulating the process of cardiac chamber ballooning have been identified, the cellular mechanisms underlying the chamber formation remain unclear. Here, we demonstrate that cardiac chambers remodel by cell neighbour exchange of cardiomyocytes guided by the planar cell polarity (PCP) pathway triggered by two non-canonical Wnt ligands, Wnt5b and Wnt11. We find that PCP signalling coordinates the localisation of actomyosin activity, and thus the efficiency of cell neighbour exchange. On a tissue-scale, PCP signalling planar-polarises tissue tension by restricting the actomyosin contractility to the apical membranes of outflow tract cells. The tissue-scale polarisation of actomyosin contractility is required for cardiac looping that occurs concurrently with chamber ballooning. Taken together, our data reveal that instructive PCP signals couple cardiac chamber expansion with cardiac looping through the organ-scale polarisation of actomyosin-based tissue tension

Phase coherence phenomena in superconducting films

Superconducting films subject to an in-plane magnetic field exhibit a gapless superconducting phase. We explore the quasi-particle spectral properties of the gapless phase and comment on the transport properties. Of particular interest is the sensitivity of the quantum interference phenomena in this phase to the nature of the impurity scattering. We find that films subject to columnar defects exhibit a `Berry-Robnik' symmetry which changes the fundamental properties of the system. Furthermore, we explore the integrity of the gapped phase. As in the magnetic impurity system, we show that optimal fluctuations of the random impurity potential conspire with the in-plane magnetic field to induce a band of localized sub-gap states. Finally, we investigate the interplay of the proximity effect and gapless superconductivity in thin normal metal-superconductor bi-layers.Comment: 13 pages, 8 figures include